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The Spider Poset Is Macaulay

✍ Scribed by Sergei L. Bezrukov; Robert Elsässer

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
326 KB
Volume
90
Category
Article
ISSN
0097-3165

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✦ Synopsis

Let Q(k, l ) be a poset whose Hasse diagram is a regular spider with k+1 legs having the same length l. We show that for any n 1 the n th cartesian power of the spider poset Q(k, l ) is a Macaulay poset for any k 0 and l 1. In combination with our recent results (S. L. Bezrukov, 1998, J. Combin. Theory Ser. A 84, 157 170) this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices, whose Hasse diagrams are trees.

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